Table 1 Derived fitting equations for the different traces found in aGST and cGST phase of the proposed analyte–Ag–Si–HfO2–Si–GST–Si structure for different wavelength and refractive index ranges.

From: Numerical analysis of hafnium oxide and phase change material-based multi-layered infrared and visible frequency sensor for biomolecules sensing application

Design

Trace

Wavelength range (\(\mathrm{\lambda in \mu m})\)

Refractive index \((\mathrm{n})\)

Fitting equation

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E1

(0.72, 0.93)

(1.91,2.38)

\(\uplambda =-24.5264{\mathrm{n}}^{3}+63.7145{\mathrm{n}}^{2}-52.5753\mathrm{n}+15.8852\)

E2

(0.78. 1.06)

(1.76,2.40)

\(\uplambda =-6.0189{\mathrm{n}}^{3}+15.0025{\mathrm{n}}^{2}-10.1467\mathrm{n}+3.3914\)

E3

(0.73,1.21)

(1.41, 2.38)

\(\uplambda =-2.6547{\mathrm{n}}^{3}+8.4055{\mathrm{n}}^{2}-6.6480\mathrm{n}+2.8008\)

E4

(0.69,1.31)

(1.31, 2.38)

\(\uplambda =4.9489{\mathrm{n}}^{3}-13.3718{\mathrm{n}}^{2}+13.5039\mathrm{n}-3.5263\)

E5

(0.81,1.49)

(1.01, 2.38)

\(\uplambda =-27.9849{\mathrm{n}}^{5}+129.8418{\mathrm{n}}^{4}-225.8289{\mathrm{n}}^{3}+179.7946{\mathrm{n}}^{2}-60.5107\mathrm{n}+5.9265\)

E6

(1.0,1.77)

(1.03, 2.38)

\(\uplambda =-117.3662{\uplambda }^{5}+858.2018{\uplambda }^{4}-2492.0735{\mathrm{n}}^{3}+3590.3699{\mathrm{n}}^{2}-2563.1039\mathrm{n}+725.5755\)

E7

(1.26,2.05)

(1.11, 2.38)

\(\uplambda =-0.3495{\mathrm{n}}^{3}+2.5379{\mathrm{n}}^{2}-3.8442\mathrm{n}+2.6359\)

E8

(1.54,2.5)

(1, 2.36)

\(\uplambda =-0.2061{\mathrm{n}}^{3}+0.7432{\mathrm{n}}^{2}+0.9396\mathrm{n}-1.5120\)

E9

(1.89,2.43)

(1.01, 1.50)

\(\uplambda =0.6666{\mathrm{n}}^{3}-4.7387{\mathrm{n}}^{2}+12.0010\mathrm{n}-9.2353\)

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E10

(0.70,0.94)

(1.87, 2.40)

\(\uplambda =-19.3064{\mathrm{n}}^{3}+50.1595{\mathrm{n}}^{2}-40.9114\mathrm{n}+12.5501\)

E11

(0.71,1.06)

(1.62, 2.40)

\(\uplambda =-10.8119{\mathrm{n}}^{3}+30.1545{\mathrm{n}}^{2}-25.5130\mathrm{n}+8.4103\)

E12

(0.86,1.23)

(1.61, 2.40)

\(\uplambda =-0.3250{\mathrm{n}}^{3}+1.1931{\mathrm{n}}^{2}+0.6615\mathrm{n}+0.3679\)

E13

(0.69,1.40)

(1.10, 2.38)

\(\uplambda =-0.1467{\mathrm{n}}^{3}+1.0458{\mathrm{n}}^{2}+0.0935\mathrm{n}+0.5689\)

E14

(0.82,1.35)

(1, 1.79)

\(\uplambda =1.1638{\mathrm{n}}^{3}-3.2300{\mathrm{n}}^{2}+4.2928\mathrm{n}-0.9897\)

E15

(1.07,1.78)

(1.01, 2.40)

\(\uplambda =95.3522{\mathrm{n}}^{5}-673.2390{\mathrm{n}}^{4}+1881.7529{\mathrm{n}}^{3}-2600.8871{\mathrm{n}}^{2}+1778.6185\mathrm{n}-480.8560\)

E16

(1.45,2.06)

(1.27, 2.4)

\(\uplambda =-3.3578{\mathrm{n}}^{3}+18.3768{\mathrm{n}}^{2}-31.3586\mathrm{n}+18.3599\)

E17

(1.60,2.46)

(1.01,2.20)

\(\uplambda =0.2730{\mathrm{n}}^{3}-2.4724{\mathrm{n}}^{2}+8.0646\mathrm{n}-6.7459\)

E18

(1.84,2.45)

(1.01,1.49)

\(\uplambda =-0.0147{\mathrm{n}}^{3}-0.2512{\mathrm{n}}^{2}+2.1507\mathrm{n}-2.0526\)

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